I wonder if your characterization of the “new Labour” voters as constituting a “narrower” church is somewhat misleading, potentially.

One sense that I had while tracking the Sanders voters in the US is that, while the average Sanders voter might be more “liberal” than the average Clinton voter, the former were also a much more heterogeneous lot: if you found a “conservative” who was willing to vote Democratic, that voter would have been a lot more likely to become a Sanders supporter than a Clinton one: it just so happens that “conservative” Democrats would have been far few to affect the aggregate numbers — or the impression that Sanders is drawing from the far left.

If my sense about the US is true, that inverts the usual sense we have of “narrow” vs. “broad”: we often imagine that inclusion of “centrists” necessarily indicates the latter. This does not need to be the case. In a sense, “centrists” are simply those who happen to be most frequently included in the winning, thus presumably the “majority” (but not necessarily), coalition if the politics is assumed to be spatial, while the “extremists” are simply those who are left out. Whether they identify with the left or the right is second order business. That Sanders drew heavily from the “left extreme” simply means that he was supported by the losers in the intra-Democratic Party struggle. That he drew, relatively speaking, heavily from the “right extreme” (for Democrats anyways) means that he drew people who were left out but are not conventional Democrats (i.e. “left”).

The workings of the UK parties make me hesitant to think that the same logic would necessarily apply without extensive modification. But the basic argument seems applicable still: that, somewhat paradoxically, the center has defined itself too narrowly and that the revolt is taking place on both edges, but, since Labour is supposed to be the left party, the left edge draws more attention. If my suspicion is right, the means for the centrists and the edgy rebels should be close (that which you find), but they would feature distinctly different distributions: the centrists would be unimodal and narrow, while the rebels would be possibly bimodal, or, at least, quite fat in their distribution. I’m not too sure where exactly the distributional differences would show up, but if possible, could you investigate this angle further?